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If 10 tickets are sold, and you and a friend buy 1 ticket each. Two winners will be

selected. The probability that your friend wins 1st prize and you second prize is:

P(event that friend wins 1st and you 2nd) = 1/10 x 1/9 = 0.01111... ≈ 1.11 %

The probability that you win 1st and your friend 2nd is the same:

P(event that you win 1st and friend 2nd) = 1/10 x 1/9 = 0.01111... ≈ 1.11 %

The probability that you and your friend win either way is the sum of both:

P(event that you and your friend win either prize) = 0.02222... ≈ 2.22 %

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